Hazard fractured his ankle in training with national side Belgium on Sunday and underwent surgery on the injury the following day.
The Chelsea winger is set to be sidelined for a minimum of eight weeks, meaning he is likely to miss the Community Shield on Sunday 6 August against Arsenal.
Vertonghen has wished his international team-mate well and has spoken to him since the incident
"I spoke to him very briefly, two days ago," the central defender said on Sky Sports.
Jan Vertonghen hopes Chelsea star Eden Hazard is fit for the start of next season Chelsea fans react as Eden Hazard gives injury update after surgery Mon, June 5, 2017
Eden Hazard has given an update on his ankle injury following surgery, and Chelsea fans are delighted
Play slideshow 1 of 11
Eden Hazard is a very positive guy and he was already smiling
Jan Vertonghen on Chelsea star Eden Hazard
"Eden is a very positive guy and he was already smiling.
"We wish him all the best and hopefully see him back at the start of next season."
The 30-year-old admits Spurs keeping their star players such as Kyle Walker and Danny Rose is crucial if they want to challenge for the title next term.
Get Quotes on Home Insurance
Jan Vertonghen says Spurs need to keep hold of their best players
"These guys showed their importance to us this season and for a couple of seasons now," he added.
"I think Tottenham has the strength and power to keep guys like that in the team these days.
"I really hope they all stay and we all push together for something very nice next season."